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El. knyga: Raven's Hat

3.80/5 (18 ratings by Goodreads)
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  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Feb-2021
  • Leidėjas: MIT Press
  • Kalba: eng
  • ISBN-13: 9780262362689
Kitos knygos pagal šią temą:
Raven's HatDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Feb-2021
  • Leidėjas: MIT Press
  • Kalba: eng
  • ISBN-13: 9780262362689
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"Introducing complex math concepts through the medium of seemingly unsolvable games"--

Games that show how mathematics can solve the apparently unsolvable.

This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.

Recenzijos

Choice 2021 Outstanding Academic Title

A book of intriguing problems that are simple to state and yet seem impossible to solve. Each problem has been carefully chosen to illustrate an important mathematical concept. The lucid explanations provide aha moments that connect the problems to key ideas in a wide variety of undergraduate courses. A wonderful book for someone who likes mathematics and likes to be challenged! Chris Bernhardt, author of Quantum Computing for Everyone   This is a fantastic book! Its full of clever and carefully constructed puzzles that will entertain any mathematically curious reader, from novice to expert. Richard J. Samworth, Professor of Statistical Science, University of Cambridge

Preface And Acknowledgments xi
1 Hat Colors And Hamming Codes
1(16)
1.1 The Game
1(2)
1.2 How Well Can a Strategy Work?
3(3)
1.3 Some Mathematics: Hamming Codes
6(3)
1.4 Solution
9(3)
1.5 Hamming Codes in Higher Dimensions
12(2)
1.6 Short History
14(1)
1.7 Practical Advice
14(3)
2 Twenty Boxes And Permutations
17(16)
2.1 The Game
17(3)
2.2 How Well Can a Strategy Work?
20(1)
2.3 Solution
21(1)
2.4 Some Mathematics: Permutations and Cycles
21(2)
2.5 Understanding the Solution
23(8)
2.6 Short History
31(1)
2.7 Practical Advice
31(2)
3 The Dovetail Trick And Rising Sequences
33(22)
3.1 The Trick
33(1)
3.2 Riffle Shuffling Cards
34(3)
3.3 Some Mathematics: Permutations
37(4)
3.4 Solution
41(2)
3.5 More Mathematics: Shuffling Distributions
43(7)
3.6 Measuring the Goodness of a Shuffle
50(2)
3.7 Short History
52(1)
3.8 Practical Advice
53(2)
4 Animal Stickers And Cyclic Groups
55(18)
4.1 The Game
55(2)
4.2 Solution for 3 Animals
57(4)
4.3 Some Mathematics: Cyclic Groups
61(3)
4.4 Variation: Colored Hats in a Line
64(6)
4.5 Short History
70(1)
4.6 Practical Advice
70(3)
5 Opera Singers And Information Theory
73(20)
5.1 The Game
73(3)
5.2 How Well Can a Strategy Work?
76(1)
5.3 Solution for 5 Singers
77(2)
5.4 Some Mathematics: Information Theory
79(9)
5.5 Variation: Ball Weighing
88(1)
5.6 Random Strategies
89(2)
5.7 Short History
91(1)
5.8 Practical Advice
92(1)
6 Animal Matching And Projective Geometry
93(16)
6.1 The Game
93(3)
6.2 Solution
96(1)
6.3 Fano Planes
96(2)
6.4 Some Mathematics: Projective Geometry
98(8)
6.5 Short History
106(1)
6.6 Practical Advice
106(3)
7 The Earth And An Eigenvalue
109(14)
7.1 The Game
109(4)
7.2 Solution
113(1)
7.3 Some Mathematics: Linear Algebra
114(6)
7.4 Short History
120(1)
7.5 Practical Advice
120(3)
8 The Fallen Picture And Algebraic Topology
123(48)
8.1 The Fallen Picture
123(2)
8.2 Solution for 2 Nails
125(1)
8.3 Dancing
125(2)
8.4 Some Mathematics: Algebraic Topology
127(7)
8.5 Solution, Continued
134(3)
8.6 Short History
137(1)
8.7 Practical Advice
137(2)
A What Do We Mean When We Write ...?
139(4)
B What Is ...
143(14)
B.1 ... a Binary Number?
143(1)
B.2 ... a Converging Sequence or Series?
144(2)
B.3 ... an Exponential Function?
146(2)
B.4 ... a Binomial Coefficient?
148(2)
B.5 ... a Probability?
150(2)
B.6 ... an Expectation?
152(1)
B.7 ... a Matrix?
153(1)
B.8 ... a Complex Number?
154(3)
C
Chapter-Specific Details
157(14)
C.1
Chapter 1: Hat Colors and Hamming Codes
157(5)
C.2
Chapter 4: Animal Stickers and Cyclic Groups
162(2)
C.3
Chapter 5: Opera Singers and Information Theory
164(3)
C.4
Chapter 6: Animal Matching and Projective Geometry
167(2)
C.5
Chapter 8: The Fallen Picture and Algebraic Topology
169(2)
References 171(4)
Index 175
Jonas Peters is Professor of Statistics at the University of Copenhagen. Nicolai Meinshausen is Professor of Statistics at ETH (Swiss Federal Institute of Technology) in Zurich.
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